The one-dimensional spin-1/2 XXZ model with the limited case of the staggered Gamma interaction which includes the staggered DM and KSEA interactions is investigated by utilizing the infinite-time evolving block decimation method in the infinite matrix product state representation. It is shown that the staggered DM interaction does not lead to any new phase but expands the XY phase. Contrasted to the DM interaction, the region of the ferromagnetic phase expands into the nematic-ferromagnetic and dimer-Haldane phases with the deconfined quantum phase transition happening in the case of KSEA interaction. We observe a pronounced effect in the entanglement entropy and Schmidt gap, the odd-bond and even-bond von Neumann entropies exhibit different values, and the value of the Schmidt gap on the even bond becomes zero in the dimer-Haldane phase. This implies that quantum entanglement and the Schmidt gap can distinguish the two degenerate ground states caused by the existence of dimerized interaction. The zero value of the Schmidt gap works as a sign of the topological phase, which is also evidenced by the string correlation. From the perspective of magnetism, the existence of chiral order and nematic order suggests the helical magnetic structure induced by Gamma interaction. By comparing the DM and KSEA interactions, it is found that DM interaction does not change ferromagnetism, whereas the KSEA interaction inhibits ferromagnetism and destroys the product state in the ferromagnetic phase. Furthermore, the behaviors of the spin structure factor for the transversal spin correlation can distinguish different phases. From an appropriate fitting exponent of the spin correlation oscillating decay, commensurate or incommensurate phases can be identified.
The one-dimensional spin-1/2 XXZ model with the limited case of the staggered Gamma interaction which includes the staggered DM and KSEA interactions is investigated by utilizing the infinite-time evolving block decimation method in the infinite matrix product state representation. It is shown that the staggered DM interaction does not lead to any new phase but expands the XY phase. Contrasted to the DM interaction, the region of the ferromagnetic phase expands into the nematic-ferromagnetic and dimer-Haldane phases with the deconfined quantum phase transition happening in the case of KSEA interaction. We observe a pronounced effect in the entanglement entropy and Schmidt gap, the odd-bond and even-bond von Neumann entropies exhibit different values, and the value of the Schmidt gap on the even bond becomes zero in the dimer-Haldane phase. This implies that quantum entanglement and the Schmidt gap can distinguish the two degenerate ground states caused by the existence of dimerized interaction. The zero value of the Schmidt gap works as a sign of the topological phase, which is also evidenced by the string correlation. From the perspective of magnetism, the existence of chiral order and nematic order suggests the helical magnetic structure induced by Gamma interaction. By comparing the DM and KSEA interactions, it is found that DM interaction does not change ferromagnetism, whereas the KSEA interaction inhibits ferromagnetism and destroys the product state in the ferromagnetic phase. Furthermore, the behaviors of the spin structure factor for the transversal spin correlation can distinguish different phases. From an appropriate fitting exponent of the spin correlation oscillating decay, commensurate or incommensurate phases can be identified.
Abstract This study investigates the quantum phase transitions and critical behaviors in the transverse Ising model with staggered Γ interaction by utilizing the infinite-time evolving block decimation method in the infinite matrix product states representation. The ground-state phase diagram shows that the system exhibits a phase transition from the transverse Néel phase to the paramagnetic phase as the transverse magnetic field increases, which are characterized by the local magnetization and non-local transverse Néel order. The chiral order and nematic order are calculated to explore the helical and nematic magnetic structure caused by the Γ interaction. From the spin-spin correlation, a modulated commensurate power-law oscillating decay behavior provides insight in analyzing the ground state characteristics of each phase. In order to study the quantum criticality, the critical exponents β , ν and central charge c are extracted and numerically consistent with the Ising class transition, demonstrating that the critical behavior in our model occurs is independent of the emergent Gamma interaction.
The quantum criticality and entanglement properties are investigated in the one-dimensional spin-1/2 transverse field Ising model with staggered Dzyaloshinsky-Moriya interaction by utilizing the infinite-time evolving block decimation method. In this model, the staggered Dzyaloshinsky-Moriya interaction does not lead any new phase, while it only appears a phase transition line between Néel phase and paramagnetic phase. The behaviors of measurements of information illustrate the quantum phase transition and the existence of factorized points. The factorization phenomena is observed in the transverse Néel phase detecting by the entanglement quantities, in which the double degenerate ground state in transverse Néel phase is preserved by the Dzyaloshinsky-Moriya interaction also evidencing from the fidelity map. From the perspective of magnetism, the existence of chiral order and transverse Néel order suggests the helical magnetic structure induced by Dzyaloshinsky-Moriya interaction. The critical exponents and central charge keep invariant and convinced that the phase transitions belong to the Ising universality class. In contrary to the systems confined within central charge c=1, although the competition between the Dzyaloshinsky-Moriya interaction and external field changes the phase transition and entanglement properties, the quantum criticality seems independent of Dzyaloshinsky-Moriya interaction.
Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation (iTEBD) method. The quantum phase transition (QPT) from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around r c ≃ 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetic correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.
We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.
Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm. The bipartite entanglement entropy can detect a transition point between the two phases. In both phases, the entanglement spectrum shows double degeneracy. We calculate the nonlocal order parameter of the bond-centered inversion in both phases, which rapidly approaches a saturation value of −1 as the segment length increases. The nonlocal order parameter of the bond-centered inversion with a saturation value −1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase. To distinguish the commensurate and incommensurate Haldane phases, the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed. As a result, the transversal spin correlations exhibit different decay forms in both phases.
Quantum phase transitions are driven by quantum fluctuations due to the uncertainty principle in many-body physics. In quantum phase transitions, the ground-state changes dramatically. The quantum entanglement, specific heat, magnetization and other physical quantities diverge according to certain functions, and show specific scaling behaviors. In addition, there is a topological quantum phase transition beyond the conventional Landau-Ginzburg-Wilson paradigm, which is relevant to emergent phenomena in strongly correlated electron systems, with topological nonlocal order parameters as a salient feature. Thus, topological order is a new paradigm in the study of topological quantum phase transitions. To investigate competition mechanism of the different quantum spin interactions, in this paper, the one-dimensional spin-1 bond-alternating Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction is considered. The DM interaction drives the quantum fluctuations resulting in a phase transition. By using the one-dimensional infinite matrix product state algorithm in tensor network representation, the quantum entanglement entropy and order parameters are calculated from the ground-state function. The numerical result shows that with the change of bond alternating strength, there is a quantum phase transition from the topological ordered Haldane phase to the local ordered dimer phase. Based on the von Neumann entropy and order parameter, the phase diagram of this model is obtained. There is a critical line that separates the Haldane and the dimer phase. The DM interaction inhibits the dimerization of the quantum spin system and finally breaks the fully dimerization. Due to the fact that the structurally symmetry of system is broken, the local dimer order exists in the whole parameter range when the bond-alternative strength parameter changes. The first derivative of the local dimer order behaves as a peak corresponding to the critical point. Furthermore, from the numerical scaling of the first derivative of dimer order and the non-local string order near the phase transition point, the characteristic critical exponents α and β are obtained, respectively. It shows that the characteristic critical exponent α decreases, and β increases gradually with the interaction strength of DM increasing. The resulting state i.e. the anti-symmetric anisotropic DM interaction produced by spin-orbit coupling, affects the critical properties of the system in the phase transition. This reveals that the competition mechanism of the quantum spin interaction, also provides some guidance for the future study of the critical behavior in topological quantum phase transition with the DM interaction.